The ALP miracle

collaboration with F. Takahashi & W. Yin

Ryuji Daido Tohoku Univ.

@PPP2017

1702.03284 JCAP05(2017)044

V

There are two unknown degree of freedom in the CDM. (except for the origin of .)

⇤

⇤

1. Introduction

•Inflaton

•Dark matter

Both are neutral and occupied a significant fraction of the energy density of the Universe.

Very flat potential for slow-roll inflation.

Cold, neutral, and long-lived.

V

Thermal history

Inflaton decays and produce radiation, while DM must be produced somehow.

inflaton

radiation

DM

⇢

Scale factor

?

Inflaton = DM ?

cf. Kofman, Linde, Starobinsky `94, Mukaida, Nakayama 1404.1880, Bastero-Gil, Cerezo, Rosa,1501.05539 see also Lerner, McDonald 0909.0520, Okada, Shafi 1007.1672, Khoze 1308.6338 for inflaton WIMP.

If the reheating is incomplete, some of inflaton condensate may remain.

DM=inflaton

radiation

Incomplete reheating!

inflaton

⇢

Scale factorThe remnant inflaton condensate due to incomplete reheating can be dark matter.

What we did

•Inflaton = DM = Axion-like particle (ALP)

•The observed CMB and LSS data fix the relation between the ALP mass and decay constant.

•Successful reheating and DM abundance point to specific values

within the reach of IAXO.

g��� = O(10�11)GeV�1m� = O(0.01) eV ,

2. Axion and InflationAxion is a pseudo NG boson, and enjoys a discrete shift symmetry.

� ! �+ 2⇡nf

Since dangerous radiative corrections are naturally suppressed, axion is compatible with inflation.

n 2 Z

V (�) = V (�+ 2⇡f)

and can be expressed as Fourier series, �� = 2⇡f

V (�) =X

n2Z

cnein�

f

The axion potential is periodic, i.e.

-1 1 2 3 4ϕ/f

0.5

1.0

1.5

2.0

V(ϕ)/Λ4

・Super-Planckian decay constant is required.

Axion and Inflation

The simplest model is the natural inflation.

Freese, Frieman, Olinto `90

・Large field inflation

・Predicted are not favored by recent observations.

•Natural inflation

(ns, r)

•Axion hilltop inflation

• Inflaton is light both during inflation and in the true min.

Flatness=longevitym2

� = V 00(�min

) = �V 00(�max

)

Hilltop inflation can be realized with two cosine terms.

-1 1 2 3 4 5

0.5

1.0

1.5

0

Odd n

Vinf(�) = ⇤

4

✓cos

✓�

f+ ✓

◆�

n2cos

✓n�

f

◆◆+ C

upside down symmetric

Czerny, Takahashi 1401.5212, Czerny, Higaki, Takahashi 1403.0410, 1403.5883

• The decay constant can be sub-Planckian. f ⌧ MP

= V0 � ��4 � ⇤4✓�

f+ (� 1)

⇤4

2f2�2 + . . .

V (�)/⇤4

(Minimal extension)

Axion and Inflation

•Axion hilltop inflation

� ' 7.5⇥ 10�14

✓N⇤50

◆�3

.

N⇤ ' 61 + ln

✓H⇤Hinf

◆ 12

+ ln

✓Hinf

1014GeV

◆ 12

ns ' 1 + 2⌘(�⇤) ' 1� 3

N⇤

Planck normalization

Spectral index

Hilltop inflation can be realized with two cosine terms.

Vinf(�) = ⇤

4

✓cos

✓�

f+ ✓

◆�

n2cos

✓n�

f

◆◆+ C

(Minimal extension)

= V0 � ��4 � ⇤4✓�

f+ (� 1)

⇤4

2f2�2 + . . .

Czerny, Takahashi 1401.5212, Czerny, Higaki, Takahashi 1403.0410, 1403.5883

-1 1 2 3 4 5

0.5

1.0

1.5

0

Odd n

upside down symmetric

V (�)/⇤4

Axion and Inflation

Spectral index

The typical inflaton mass: m� ⇠ ✓13⇤2

f= O(0.1)Hinf

-0.06-0.04-0.020.00 0.02 0.04 0.06 0.08

-0.01

0.00

0.01

0.02

0.03

0.04

(κ-1)×(f/Mpl)-2

θ×(f/Mpl)-3

cf. ns ' 1 + 2⌘(�⇤)

ns = 0.968± 0.006

Relation between and m� f

The Planck normalization of density perturbation and the spectral index fix the relation between and ,m� f

: Planck normalization

: Friedman eq.

: Scalar spectral indexcf. ns ' 1 + 2⌘(�⇤)

� ⇠✓⇤

f

◆4

⇠ 10�13

⇤4 ⇠ H2infM

2pl

m� ⇠ 0.1Hinf

f ⇠ 5⇥ 107 GeV⇣n3

⌘1/2 ⇣ m�

1 eV

⌘0.51

KSVZ

QCD axion

IAXOALPS-II

10-4 10-3 10-2 10-1 100 101 102 103

CAST HB

10-14

10 -13

10 -12

10 -11

10 -10

10 -9

m [eV]φ

CMB τ

EBL

X-ray

Telescopes

g��� =c�↵

⇡f

RD, Takahashi, and Yin 1702.03284 Limits taken from Essig et al 1311.0029

Successful inflation

c� =X

i

qiQ2i

i ! ei�qi�5/2 i

� ! �+ �f

L =g���4

�Fµ⌫F̃µ⌫

Mass and coupling to photons

The inflaton oscillates about in a quartic potential.�min = ⇡f

-1 1 2 3 4 5

0.5

1.0

1.5

0

m2e↵(t) = V 00(�amp)The effective mass,

with time, and so, decay and dissipation become inefficient at later times.

= 12��2amp decreases

Incomplete reheating

3. Reheating and ALP DM

-1 1 2 3 4 5

0.5

1.0

1.5

0

Inflaton (ALP) condensate

Photons, SM particles

Decay & dissipation

Remnant

ALP Dark Matter

3. Reheating and ALP DM

⇠ ⌘ ⇢�⇢� + ⇢R

����after reheating

・Reheating✓The decay rate into two photons:

-1 1 2 3 4 5

0.5

1.0

1.5

0

✓The dissipation rate is roughly estimated ascf. Moroi, Mukaida, Nakayama and Takimoto,1407.7465

�dec(� ! ��) =c2�↵

2

64⇡3

m3e↵

f2

vuut1� 2m(th)

�

me↵

!2

m2e↵(t) = V 00(�amp) = 12��2

amp

m(th)� ⇠ eT

�

�

�

�dis,� = Cc2�↵

2T 3

8⇡2f2

m2e↵

e4T 2

�

�

e�

e+

⇠⇢tot

H ' �dec + �dis

Inflation

Radiation

DM

Scale factor

⇢The remnant inflaton condensate is expressed by

⇠ ⌘ ⇢�⇢� + ⇢R

����after reheating

・Reheating

g��� & 10�11 GeV�1

Solving following equations, we found

⇠ . O(0.01)for successful reheating .

KSVZ

QCD axion

IAXOALPS-II

10-4 10-3 10-2 10-1 100 101 102 103

CAST HB

10-14

10 -13

10 -12

10 -11

10 -10

10 -9

m [eV]φ

CMB τ

EBL

X-ray

Telescopes

Successful inflation

Successful reheating

/ (�� �min)4

/ (�� �min)2

Quadratic

Quartic

After the reheating, decreases like radiation until the potential becomes quadratic.

⇢�

•ALP condensate as CDM

w ⌘ P

⇢=

n� 2

n+ 2cf. for �n

zc & O(105) by SDSS and Ly-alphaDM should be formed before

SM radiation

⇢�

quartic quadraticScale factor

Matter-radiation equality

zc zeq ⇠ 3000

DM

Sarkar, Das, Sethi, 1410.7129

⇠ . 0.02

✓g⇤s(TR)

106.75

◆ 13✓

3.909

g⇤s(Tc)

◆ 13✓⌦�h2

0.12

◆✓5⇥ 105

1 + zc

◆.

•ALP condensate as CDM

•ALP condensate as CDM

⇢�

s

' 3

4⇠

34m�TRp2�fx

m� ' 0.07x�1

✓⇠

0.01

◆� 34✓⌦�h

2

0.12

◆eV,

& 0.04x�1

✓106.75

g⇤s(TR)

◆ 14✓g⇤s(Tc)

3.909

◆ 14✓⌦�h

2

0.12

◆ 14✓

1 + zc

5⇥ 105

◆ 34

eV,

SM radiation

⇢�

quartic quadraticScale factor

Matter-radiation equality

zc zeq ⇠ 3000

DM

Sarkar, Das, Sethi, 1410.7129

KSVZ

QCD axion

IAXOALPS-II

10-4 10-3 10-2 10-1 100 101 102 103

CAST HB

10-14

10 -13

10 -12

10 -11

10 -10

10 -9

m [eV]φ

CMB τ

EBL

X-ray

Telescopes

Successful inflation

Successful reheating

DM abundance

KSVZ

QCD axion

IAXOALPS-II

10-4 10-3 10-2 10-1 100 101 102 103

CAST HB

10-14

10 -13

10 -12

10 -11

10 -10

10 -9

m [eV]φ

CMB τ

EBL

X-ray

Telescopes

Successful inflation

Successful reheating

HDM constraint

DM abundance

KSVZ

QCD axion

IAXOALPS-II

10-4 10-3 10-2 10-1 100 101 102 103

CAST HB

10-14

10 -13

10 -12

10 -11

10 -10

10 -9

m [eV]φ

CMB τ

EBL

X-ray

Telescopes

Successful inflation

Successful reheating

DM abundance

HDM constraint

KSVZ

QCD axion

IAXOALPS-II

10-4 10-3 10-2 10-1 100 101 102 103

CAST HB

10-14

10 -13

10 -12

10 -11

10 -10

10 -9

m [eV]φ

CMB τ

EBL

X-ray

Telescopes

Successful inflation

Successful reheating

The ALP miracle!DM abundance

HDM constraint

Summary

•Inflaton = DM = Axion-like particle (ALP)

•The observed CMB and LSS data fix the relation between the ALP mass and decay const.

•Successful inflation, reheating and DM abundance point to

within the reach of IAXO.

g��� = O(10�11)GeV�1m� = O(0.01) eV ,

KSVZ

QCD axion

IAXOALPS-II

10-4 10-3 10-2 10-1 100 101 102 103

CAST HB

10-14

10 -13

10 -12

10 -11

10 -10

10 -9

m [eV]φ

CMB τ

EBL

X-ray

Telescopes